This document discusses strategies for increasing student engagement in online math classes. It begins by addressing common fears instructors have about teaching online and emphasizes redefining the instructor's role from lecturer to coach. Five key strategies are presented: 1) maximize student-student interaction, 2) intervene early with students who are struggling, 3) include non-routine questions and discussion prompts, 4) teach students how to communicate mathematically online, and 5) include synchronous activities using video conferencing tools. The document provides examples and resources to implement each strategy. The overall message is that with the right approaches, engagement and outcomes can be improved compared to traditional expectations of online math instruction.

1. ACTIVE LEARNING: How to Increase
Engagement in Online Math Classes to a
Level You Never Thought Possible!
Overcome students’ predilection to passivity,
create a pathway to equity and develop
confident, motivated students
By Fred Feldon, Professor of Mathematics, Coastline College
March 18, 2022

2. This presentation is available at
https://www.slideshare.net/ffeldon

4. Source: Tech for Teaching https://t4t.blog.ryerson.ca/2020/09/15

5. The Biggest Fears About Engaging Students Online
• I can’t see their faces
• I can’t call on students
• I can’t do group work
• There’s no whiteboard
• I can’t communicate using discipline notation
• Students can’t communicate using discipline notation
• I have to water down the material
• I have to do Zoom meetings
• No one’s gonna attend my Zoom meetings
• No one’s gonna participate in my Zoom meetings
• I can’t chat with students one-on-one
• I can’t cover all the material
• They’re gonna drop/fail
• My success rates will go down
• They’re gonna cheat with online exams

6. Redefine Your Role
Good Teachers = Good Coaches
-- Maria Andersen, busynessgirl.com

7. -- Maria Andersen, busynessgirl.com
Illustrations by Mat Moore

8. The Results
• YOU will discover the joy of doing what is
uniquely human and more interactive, rather
than simply deliver lectures and work examples
• YOU will have more time to interact personally with
students, to mentor, advise, review individual
work, and answer questions
• YOU will better understand how
students think and learn
• YOU will raise the collective
level of knowledge of your
class
Tim Gunn, Fashion Consultant, Project Runway & Making the Cut

9. Strategy #1
Maximize student-to-student
interaction.

10. Learning results from what
the student does and
thinks… Our job is to create
the conditions that prompt
students to do the work of
learning.”
-- Herbert Alexander Simon, 1916-2001

11. The Holy Grail
“Getting students to interact with one
another, instead of responding individually
to the instructor, might be the holy grail of
class discussion.”
David Gooblar, University of Iowa, The Chronicle of Higher Education,
November 5, 2018, https://www.chronicle.com/article/The-Holy-
Grail-of-Class/245009

12. Nicholas Bloom, Professor of
Economics, Stanford University,
2022
https://www.kqed.org/
mindshift/54486/how-
collaboration-unlocks-
learning-and-lessens-
student-isolation

13. Active Learning Promotes EQUITY
https://leginfo.legislature.ca.gov/faces/codes_displayText.xhtml?lawCode=EDC&division=7.&title=3.&part=48.&chapter=2.&article=1.5.

14. https://www.cccpathwaystoequity.com/
https://visionresourcecenter.cccco.edu/

15. NYU Steinhardt Zoom Active Learning Activities
• One Minute Paper
• Muddiest (or Clearest) Point
• Clarification Pause
• Chat Bowl
• DIY Quiz Questions
• Turn and Talk
• Show and Tell
• Two Truths & a Lie
• Jigsaw Group Discussion
• Can I See Yours
• Cooperative Groups
• Active Review
• Think, Pair, Share
• Games (e.g. Jeopardy)
• Interview Reports
• Guest Presenters
https://sites.google.com/nyu.edu/nyu-steinhardt-
toolkit/instructional-activities/zoom-activities

16. Where Do I Get Ideas From?

17. “Fred, get your butt on
Twitter and Facebook!”
Maria Andersen to Fred Feldon, 2006
Where Do I Get Ideas From?

18. • Peter Keep @MathProfPeter
• Kelly Spoon @KellyMSpoon
• Melissa D @Dean_of_Math
• Mashup Math @mashupmath
• Jay Chow @mrchowmath
• Peter Liljedahl @pgliljedahll
• NCTM @NCTM
• MAA @maanow
• AMS @amermathsoc
• AMATYC @MathAMATYC
• Sunil Singh @Mathgarden
• Jim Noble @teachmaths
• Michelle Pacansky-Brock @brocansky
• Maths Jam @MathsJam
• NRICH Maths @nrichmaths
• Desmos.com @Desmos
• Dan Meyer @ddmeyer
• Luke Walsh @LukeSelfwalker
• The Carnival of Math @CarnivalOfMath
• Numericalguy @numericalguy
• Media4Math @media4math
• Fraction Talks @FractionTalks
• TED-Ed @TED_ED
• MindShift @MindShiftKQED
• Mathgrrl @mathgrrl
• MathFeed @MathFeed
• EdSurge Higher Ed @HigherEdSurge
• Online Learning Consortium @OLCToday
• Francis Su @mathyawp
• James Tanton @jamestanton
• Howie Hua @howie_hua
• Vi Hart @vihartvihart
• Philip Uri Treisman @uritr
• Jo Boaler @joboaler
• Annie Murphy Paul @anniemurphypaul
• Sara VanDerWerf @saravdwerf
• Robert Kaplinsky @robertkaplinsky
• Rob Eby math dude @RobEbymathdude
• Alice Keeler @alicekeeler
• Alexander Bogomolny @CutTheKnotMath
• TPSE Math @tpsemath
• WODB? Math @WODBMath
• Explore MTBoS @ExploreMTBoS
• Open Middle @openmiddle
• MSRI @mathmoves
• Karen Costa
@karenraycosta
• Keith Devlin
@profkeithdevlin
• Eric Mazur @eric_mazur
• Fawn Nguyen
@fawnpnguyen
• Math Prof
@mathematicsprof
• Tim Brzezinski
@TimBrzezinski
• Citizen Math
@citizen_math
• Math for America
@MathforAmerica
• Center of Math
@centerofmath
• Chronicle of Higher
Education @chronicle
• Republic of Mathematics
@republilcofmath

22. Bumper
Ball

23. Ear
Eye
Toe
Leg
Hip
Toe
Arm
Rib
Abs
Jaw
Gum
Gut
Cap
Pit
Ass
ACL
MCL
Knee
Heel
Foot
Tooth
Butt
Three Letter Body Parts

24. Strategy #2
Intervene early: 80/20 Rule,
affective domain

25. Intervene Early
“Not taking early action to help
struggling or procrastinating students
could have dire consequences for their
performance.”
Detecting and Intervening When Students Procrastinate: New Data
for Instructors, McGraw Hill White Paper Series 2022,
https://info.mheducation.com/Procrastination-White-Paper.html

26. Intervene Early
Relationship Between Procrastination
and Course Grades

27. Intervene Early
“Dear Students -- How are you? The first week of class ends on
Sunday. If you received this email, it means you have not yet
submitted or not yet passed any assignments in the class. State law
requires professors to drop students who are No Shows or Inactive.
You are in danger of being dropped from the class. I’m trying to
prevent that. Be sure to submit at least the first homework
assignment with a grade of C (70%) or better as soon as possible. If
you have any questions, please post a message on the Discussion
Board. I check it every day. I or another student will reply right
away. We’re all here to help each other. Good luck. I’ll see you
online! -- Your Instructor, Fred Feldon, ffeldon@coastline.edu

28. Intervene Early
“Dear Students -- How are you? The second week of class is now half
over. If you received this email, it means you have NOT yet submitted or
NOT yet passed any assignments in the class. As I mentioned last week,
State law requires professors to drop students who are No Shows or
Inactive. Therefore, you’ve been dropped from the class.
Having said that, it’s not too late. If you’d like to catch up and be
reinstated in the class, send me an email. I’ve built a lot of flexibility into
the class. You can catch up without losing any points. Or just remain
dropped from the class and try again another semester. Let me know
what you decide, and if there’s anything I can do to help. I look forward
to hearing from you! -- -- Your Instructor, Fred Feldon,
ffeldon@coastline.edu

29. Spend
of your time
Helping the
of the students who
need it the most!

31. “Inferential analysis showed a significant
impact on community college math course
grade success when ADI was implemented
while controlling for gender, ethnicity, and
cumulative GPA.”
Affective Domain Intervention and
Its Impact on Community College Success in Math
Dustin Silva, EdD, College of the Canyons, Univ. of La Verne, May 2020
https://www.proquest.com/openview/5af6fef9a34ed4efbe63905d83618ddc

32. Randomized experiments have found that seemingly
“small” social-psychological interventions in
education—that is, brief exercises that target
students’ thoughts, feelings, and beliefs—can lead to
large gains in achievement and sharply reduce
achievement gaps even months and years later.”
Yeager and Walton, Review of Educational
Research, p. 267, June 2011

33. Fred’s 25+ (Now at 44!)
Open-Ended Discussion Prompts
https://docs.google.com/document/d/1AnFLJuPeTwOKKb2YyB0-V2wlIbX4xupsOWwmDMZAixs

34. Strategy #3
Include non-routine questions
and discussion prompts.

35. “Avoid the bulimic* method of education…”
*Overeating, followed by vomiting -- Dr. Stuart Firestein, 2013,
https://www.ted.com/talks/ stuart_firestein_the_pursuit_of_ignorance#t-876778

36. Questions With a Low Floor/High Ceiling
Questions that stretch your conceptual knowledge…

37. Questions With No One, Right Answer
Questions That Aren’t “Googleable,” that engage
Bloom’s Higher Order Thinking Skills (HOTS)

38. A green square is 8 cm on a side. Determine
the area of a red square if a blue circle fits
exactly into the green square and the red
square just fits inside an orange circle, two
of which just fit into the blue circle.
Questions That Are Fun!

40. Sources for Non-Routine Problems That Stimulate Discussion
Books
Math Contests Grades 4-6, 7-8 and Algebra, by Conrad & Flegler, Math League Press
Math Contests High School, by Conrad & Flegler, Math League Press
Can You Solve My Problems? By Alex Bellos Math Puzzles Vol. 1, 2 and 3 by Presh Talwalkar
Principles to Actions: Ensuring Mathematical Success for All, NCTM
The Scientific American Book of Mathematical Puzzles and Diversions, by Martin Gardner
What Students Abroad Are Expected To Know About Mathematics: Exams from France, Germany and Japan
Empowering Students by Promoting Active Learning in Mathematics, NCTM
Challenging Math Problems, by Terry Stickels
Websites
http://mathforum.org/problems_puzzles_landing.html http://blog.mrmeyer.com
http://cemc.uwaterloo.ca/resources/potw.php http://donsteward.blogspot.co.uk
http://www.mathleague.com https://ed.ted.com https://www.facebook.com/graphsintheworld
https://www.mathcounts.org/resources/problem-of-the-week http://www.onetwoinfinity.ca
https://www.math.purdue.edu/pow https://mindyourdecisions.com
http://orion.math.iastate.edu/ehjohnst/PoW/PoW.html
http://www.numberphile.com http://www.openmiddle.com
http://www.sixtysymbols.com http://www.estimation180.com
http://mathmistakes.org https://twitter.com/ExploreMTBoS (Math Twitter Blogosphere)
http://www.sciencealert.com https://twitter.com/MathVault
http://www.iflscience.com http://wodb.ca (Which One Doesn’t Belong)
http://www.ted.com http://www.visualpatterns.org
http://www.smartereveryday.com http://mathquest.carroll.edu/
https://www.youtube.com/channel/UC1_uAIS3r8Vu6JjXWvastJg (Mathologer)
Journals
Journal for Research in Mathematics Education, NCTM
Mathematics Teacher, Monthly Calendar Problems, NCTM
Mathematics Teacher Learning & Teaching PK-12, Problems to Ponder, NCTM
By Fred Feldon
Coastline College
https://www.screencast.com/
t/I2QXaKYgCyQx

41. Strategy #4
Teach students how to
communicate mathematically
online using discipline notation.

43. Digital Tools for STEM Professors
Computer Tablet with apps such as OneNote,
Evernote, Nebo, FluidMath, ScrbleInk, Journal,
Xournal − to copy, paste, annotate, etc.
Microsoft Surface

44. Computer Software
For STEM Professors

45. But What About the
Students??

46. Students write their work by hand and send you a
multi-page PDF file using a free mobile scanning app
See video https://youtu.be/UkYlGa3y4tk
*CamScanner, Microsoft OfficeLens, AdobeScan, Evernote, Abbyy FineScanner

47. Students use thick Sharpie pens to write
with, hold their paper up to the web cam
“Graph this parabola and
show me the vertex.”

48. Students show work using markers and an individual
mini-whiteboard. Hold it up to their webcam.
$10-15

49. Students can use screen capture software
to embed HTML code or an image into the
body of a Discussion Board message

50. Strategy #5
Include synchronous activities with
microphones, webcams and the
appropriate use of breakout rooms

51. Replicate the Classroom
Synchronous times for students getting together can
replace face-to-face classes, with students required to
attend. They might push back in the beginning, but then
they end up enjoying it.

52. Tips for Success, Equity and Inclusion
• First day of class post schedule of meetings and explain:
 “Under federal code of regulations, instructors are required to verify
the identity of students who participate in the class. Appropriate
methods such as webcams, microphones and electronic proctoring of
exams may be required.”
• Allow opt out of webcam on a case-by-case, meeting-by-meeting basis
• Schedule meeting dates and times at your convenience. It’s impossible to
satisfy everyone: 5 mid-week evening Zoom meetings 7:30-8:30 pm every 2-
3 weeks or so worked for me
• Record the meetings so students who miss it live can watch the recording
• Show up 15 minutes early to greet students
• Don’t try to cover or teach everything—content is everywhere (see next
slide); preload content you know students struggle with the most (use IA)
• If time ends, use discussion board to follow up so everyone can benefit
• Participation in these meetings and discussion boards is 15% of their grade
in the class
• Contact every student who missed a meeting and didn’t watch the
recording

53. PatrickJMT
Content Is Everywhere!

54. A Few Tips for Breakout Rooms:
• Before breaking students into groups give them a
couple minutes to think deeply about the problem and
make notes, otherwise they may have nothing to
contribute to the group
• If asking for a response in the Chat, tell students to
begin typing but do NOT hit Enter until you give the
signal, to eliminate a “conga line” of responses that is
students just copy each other
• Hop in and out of the small groups to gather
information on what your students are thinking; ask
them to SHOW YOU what they’re working on

55. https://www.facebook.com/100013305873659/videos/1171288096658042/

56. Source: https://www.teachingeffectivelywithzoom.com/

57. Side Bar—Webcams?
Kindergarten Teacher Mackenzie Adams
Goes Viral on TikTok - See 3-min video
https://youtu.be/ujjNIjqKSSU

58. From My Course Website…

59. From My Course Website…

60. The Big Takeaways For Success!
• Maintain rigor
• Don’t drain your time or energy creating content;
use what’s out there
• Offer an abundance of mentoring, flexibility and
compassion; 80/20 Rule
• Pay deliberate attention to the affective domain
• De-emphasize concern about cheating; think about new
ways of assessing

61. New Ways of Assessing
https://youtu.be/whoaNY1mlgE https://youtu.be/DpLeJFtwfCo
https://www.francissu.com/post/7-exam-
questions-for-a-pandemic-or-any-other-time
https://medium.com/@jamestanton/covid-19-exposes-
mathematics-education-inadequacies-a-modicum-of-
secret-relief-for-educators-48490c44d649

62. The Big Takeaways For Success!
• Maintain rigor
• Don’t drain your time or energy creating content;
use what’s out there
• Offer an abundance of mentoring, flexibility and
compassion; 80/20 Rule
• Pay deliberate attention to the affective domain
• De-emphasize concern about cheating; think about new
ways of assessing
• Add synchronous activities with active learning, student
participation and breakout groups
• Have students use Sharpies or whiteboards
• Have fun. You got this!

63. Thank You!
ffeldon@coastline.edu